Adjustable compliant mechanism

ABSTRACT

Constant force mechanisms and adjustable constant force mechanisms are described having two movable sliders constrained along two perpendicular axes and each abutting a resilient member. The mechanisms are adapted to produce an output force that is constant for a given input force. However, when an equilibrium position of one of the two resilient members is adjusted for a given mechanism, a different output force will result. Micro-compliant mechanisms are also described in which the resilient members may be made from one or more different elastomers.

Compliant mechanisms and constant force mechanisms capable of producinga constant force for the entire range of motion are generally discussedherein with specific discussions extended to constant force mechanismsthat are adjustable.

BACKGROUND

Mechanisms with interesting force-deflection characteristics have alwaysintrigued engineers and scientists and thus have been a subject ofon-going research. Mechanisms using linear springs to give increasedforce outputs with greater input displacements have been widely knownand researched. In some applications, the output force may be desired tostay constant with a change in the input displacement. Such situationsarise in applications such as robotic grasping, preventing damage tomachine tools or end-effectors due to unforeseen position errors,biomedical applications, haptic devices, and micro-grasps. Thesemechanisms are referred to as “constant-force” mechanisms. An exemplaryconstant force-mechanism is described in U.S. Pat. No. 5,649,454 (Midhaet al.), its contents are expressly incorporated herein by reference.

A constant-force mechanism is designed to produce a constant-force forthe entire range of motion. This mechanism is a compliant mechanism asit gains movement from parts that flex, bend, or have a resiliency andin addition produces a desired constant-force output at all times. Aconstant force can be generated using hydraulic, pneumatic, andelectrical device units, or even with a negator spring. But, frompractical design considerations for micro applications, these solutionsmay not be possible. For micro applications, a solution applicable to amechanical linkage system is needed which does not incorporate a powersource.

Accordingly, it would be more useful to engineers and scientists alikeif the constant-force output could be adjusted and that it has microscale applications. Accordingly, there is a need for a variable oradjustable constant-force mechanism for increased versatility and onewhich has a number of different applications including micro-scaleapplications.

SUMMARY

The present invention may be implemented by providing a compliantmechanism comprising two support structures each comprising atranslational axis mounted perpendicular to one another; a resilientmember comprising a length attached to a slidable structure positionedon each support structure; a first link pivotally connected directly orindirectly to each of the slidable structures, and an adjustment blockattached to one of the structures for changing the length of theresilient member of that structure.

Alternatively, the present invention may also be practiced by providinga compliant mechanism comprising an input structure, two resilientmembers each comprising a length connected directly or indirectly to theinput structure and wherein the two resilient members are mountedparallel to one another along a lengthwise direction, a third resilientmember comprising a length mounted directly or indirectly to the inputstructure with its length generally perpendicularly to the lengths ofthe two resilient members; and a plurality of links connected directlyor indirectly to the input structure.

In another aspect of the present invention, there is provided acompliant mechanism for producing a constant force during a range ofmotion of the mechanism comprising a first structure comprising a firstmovable slider adapted to move along a first linear direction, a firstresilient member comprising a length acting on the first slider so thatthe first slider experiences a pushing force from the first resilientmember during movement of the first slider along at least a portion ofthe first linear direction, a second structure comprising a secondmovable slider adapted to move along a second linear direction, a secondresilient member comprising a length acting on the second slider so thatthe second slider experiences a pushing force from the second resilientmember during movement of the second slider along at least a portion ofthe second linear direction; a link comprising a length in pivotablerelationship, either directly or indirectly, with both the first sliderand the second slider; and an adjustment mechanism mechanically coupledto either the first resilient member or the second resilient member foradjusting the length of the first resilient member or the secondresilient member.

In still yet another aspect of the present invention, there is provideda compliant mechanism comprising a slider connected to a first link by afirst joint, the first link connected to a second link by a secondjoint, and the second link connected to a third link by a third joint,wherein the first link and second link are at a first angle to oneanother during a first position; the third joint is fixed to a firstbase; the slider is movable over a second base; and the first angle isadjustable to a second angle by moving either the first base or thesecond base.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features and advantages of the present invention willbecome appreciated as the same become better understood with referenceto the specification, claims and appended drawings wherein:

FIG. 1 is a semi-schematic diagram of a constant force mechanismprovided in accordance with aspects of the present invention;

FIG. 2 is a semi-schematic diagram of the constant force mechanism ofFIG. 1 with the sliders in their respective home positions;

FIG. 3 is a semi-schematic diagram of the constant force mechanism ofFIG. 1 having a force applied to the horizontal slider to produce anangular displacement for the link;

FIG. 4 is a semi-schematic diagram of an adjustment to the length of thehorizontal spring;

FIG. 5 is a semi-schematic diagram of an alternative constant forcemechanism provided in accordance with aspects of the present invention;

FIG. 6 is a semi-schematic diagram of an adjustable constant forcemechanism comprising the constant force mechanism of FIG. 5 and anadjustable block;

FIG. 7 is a semi-schematic diagram of a micro-compliant mechanismprovided in accordance with aspects of the present invention;

FIG. 8 is reproduced from FIG. 1 a of U.S. Pat. No. 5,649,454 (Midha etal.);

FIG. 9 is a vector analysis diagram of the constant force mechanism ofFIG. 3;

FIG. 10 is a graph showing the relationship between the output force ofthe constant force mechanism and the length of the spring; and

FIG. 11 is a graph showing results obtained from an experiment on theadjustable constant-force mechanism.

DETAILED DESCRIPTION

The detailed description set forth below in connection with the appendeddrawings is intended as a description of the presently preferredembodiments of an adjustable constant force mechanism provided inaccordance with practice of the present invention and is not intended torepresent the only forms in which the present invention may beconstructed or utilized. The description sets forth the features and thesteps for constructing and using the adjustable constant force mechanismof the present invention in connection with the illustrated embodiments.It is to be understood, however, that the same or equivalent functionsand structures may be accomplished by different embodiments that arealso intended to be encompassed within the spirit and scope of theinvention. Also, as denoted elsewhere herein, like element numbers areintended to indicate like or similar elements or features.

Referring now to FIG. 1, a constant-force mechanism provided inaccordance with aspects of the present invention is shown, which isgenerally designated 10. In an exemplary embodiment, the constant forcemechanism 10 (hereinafter “CFM”) comprises two sliders, a first orhorizontal slider 12 and a second or vertical slider 14, two springs 16,18, and a rigid link or connecting rod 20. The directional orientationgiven to the sliders is for reference purposes only as the sliders maybe rotated from horizontal or vertical.

In one exemplary embodiment, the first horizontal spring 16 has a normalor undeflected length l₁, the second vertical spring 18 has a normallength l₂, and the link 20 has a fixed length l₃. The sliders 12, 14 arepositioned such that they are constrained and slide perpendicular to oneanother along the respective first and second axes 26, 28. The rigidlink 20 is connected to the two sliders 12, 14 by way of two rotaryjoints 22, 24. The rotary joints are revolute-type joints as they canrotate or pivot without generating, at least significantly, a torsionalmoment. Exemplary revolute-type joints may include rivets, bolts, pins,and equivalent structures.

In a preferred embodiment, the sliders 12, 14 should slide freely toavoid or eliminate inertia and friction effects. As further discussedbelow, a working model may incorporate linear ball bearing slides 17, 19(e.g., drawer slides) and slotted guide-ways to facilitate sliding thesliders along the two axes 26, 28. When the bearings are incorporated,the slides 12, 14 move with negligible friction and produce minimalinertia effects. The slides 12, 14 may be attached to the linear ballbearings slides 17, 19 through any number of mechanical connections. Theslides may incorporate any number of configurations including a solidblock, a block comprising curved surfaces, a cylinder, and may be madefrom metal, plastic, fiberglass, delrin, a polymer, or theirequivalents.

Referring now to FIG. 2, an initial or starting configuration for themechanism 10 is shown. In this and the following configurations, theconstant force mechanism concept will be described. In the initialconfiguration, both springs 16, 18 are in an undeflected position, andboth sliders are in their home positions H1, H2, which is the positionalong the two axes 26, 28 in which no force is imparted by the sliderson the springs to axially deflect the springs.

From the initial configuration, if a force F is applied to the firstslider 12, it will move the slider 12 away from the home position H1 tocompress the first spring 16 (FIG. 3). Concurrently therewith, the link20 transfers a portion of the applied force F to the second slider 14and moves the slider away from its home position H2 to compress thesecond spring 18. At some finite point in time, the rigid link 20,having length l₃, makes an angle Θ₃ with the horizontal or first axis26. In practice, the applied force can be a force generated by a userof, for example, a weight machine or an exercise machine. The force canbe applied directly to the first slider 12 or through a mechanical link,such as a bar, a strap, a handle, a belt, a chain, a cable, etc.

For a one-degree of freedom mechanism 10 shown in FIG. 3, the mechanismmay be mathematically described as follows:

i) Generalized Coordinates: Θ₃

ii) Virtual Displacements: δΘ₃, δx, δy, where δx, and δy are functionsof δΘ₃, written asδx=f(δΘ₃),δy=f(δΘ₃)  (1)

In FIG. 9, the mechanism of FIG. 3 is shown in vector analysis form.

From the vector loop method for the mechanism shown in the vectordiagram, the kinematics of the mechanism can be written:

$\begin{matrix}\left. \begin{matrix}{{l_{1} + {l_{3}\cos\;\Theta_{3}}} = 0} \\{{0 + {l_{3}\sin\;\Theta_{3}}} = {- l_{2}}}\end{matrix} \right\} & (2) \\{{or},{l_{1} = {{- l_{3}}\cos\;\Theta_{3}}},{l_{2} = {{- l_{3}}\sin\;\Theta_{3}}}} & (3)\end{matrix}$

Differentiating the equations, it follows:i ₁ =l ₃ sin Θ₃{dot over (Θ)}₃ ,i ₂ =−l ₃ cos Θ₃{dot over (Θ)}₃  (4)

In terms of virtual displacements, the equations can be rewritten as:

$\begin{matrix}\left. \begin{matrix}{\overset{.}{x} = {{l_{3}\sin\;\Theta_{3}{\overset{.}{\Theta}}_{3}} = {\overset{.}{l}}_{1}}} \\{\overset{.}{y} = {{{- l_{3}}\cos\;\Theta_{3}{\overset{.}{\Theta}}_{3}} = {\overset{.}{l}}_{2}}}\end{matrix} \right\} & (5) \\{{Therefore},{\frac{\overset{.}{x}}{\overset{.}{y}} = {{- \tan}\;\Theta_{3}{or}}},{\overset{.}{y} = \frac{- \overset{.}{x}}{\tan\;\Theta_{3}}}} & (6)\end{matrix}$

Assuming the initial configuration is as given in FIG. 2, and thenapplying the Principle of Virtual Work, the total work done is given by:δW=−Fδx+[−k ₁(l ₁ −l ₃)]δx+[−k ₂(l ₂)]δy  (7)

In case of equilibrium, the change in work is zero. Thus, the equationmay be written as follows:−Fδx+[−k ₁(l ₁ −l ₃)]δx+[−k ₂(l ₂)]δy=0  (8)

Substituting equations (3), (5), and (6), equation (8) can be rewrittenas:

$\begin{matrix}{{{F{\overset{.}{l}}_{1}} + {{k_{1}\left( {{{- l_{3}}\cos\;\Theta_{3}} - l_{3}} \right)}{\overset{.}{l}}_{1}} + {{k_{2}\left( {{- l_{3}}\sin\;\Theta_{3}} \right)}\left( \frac{- 1}{\tan\;\Theta_{3}} \right){\overset{.}{l}}_{1}}} = 0} & (9)\end{matrix}$

By expanding the terms, the equation becomes:

$\begin{matrix}{{{{F{\overset{.}{l}}_{1}} - {k_{1}l_{3}{\overset{.}{l}}_{1}\cos\;\Theta_{3}} - {k_{1}l_{3}{\overset{.}{l}}_{1}} + {k_{2}l_{3}{\overset{.}{l}}_{1}\sin\;\Theta_{3}\frac{\cos\;\Theta_{3}}{\sin\;\Theta_{3}}}} = 0}{{or},{{{F{\overset{.}{l}}_{1}} - {k_{1}l_{3}{\overset{.}{l}}_{1}\cos\;\Theta_{3}} - {k_{1}l_{3}{\overset{.}{l}}_{1}} + {k_{2}l_{3}{\overset{.}{l}}_{1}\cos\;\Theta_{3}}} = 0}}} & (10)\end{matrix}$

If both the horizontal and vertical springs have the same materialproperties and the same stiffness, then,k₁=k₂  (11)

Substituting equation (11) in equation (10) and eliminating the commonterms, the equation becomes:F=k₁l₃  (12)

which is a constant-force and is dependent only on the stiffness of thehorizontal spring 16 and the length of the rigid link l₃ connecting thetwo sliders 12, 14. Because both the stiffness and the length areconstant, the force is therefore constant during the entire range ofmotion of the mechanism 10.

In a preferred embodiment, a constant force mechanism is provided inwhich the magnitude of the constant-force output may be actively changedto obtain a different constant-force output. This is termed as anadjustable constant-force mechanism (ACFM) having an adjustableconstant-force output. In one exemplary embodiment, the adjustment maybe made by actively changing the length of the horizontal spring 16, asshown in FIG. 4.

In the schematic diagram of FIG. 4, the horizontal spring 16 is shownsecured to a fixed or rigid first node 30, which in the FIG. 2configuration would be the furthest point on the first axis 26 fixed bythe rigid link 20. The spring 16 is secured to a second node 32 at itsopposite end, which is attached to an adjustable block 34. Theadjustable block 34 is adapted to move the second node 32 along a givenaxis via moving a link 36 that is attached to the node. Assuming thenthat the adjustable block 34 is adjusted to move a distance r_(des)(where “des” is desired) to a second position 34 a, the adjustment willcause a corresponding movement in the second node 32 to a secondposition 32 a and will likewise shorten the spring 16 by the samedistance. This movement, in effect changes, the equilibrium position ofthe spring 16, as further discussed below.

Referring again to equation (12), the movement of the spring by adistance ram will result in the following equation:F _(des) =k ₁(l ₃ +r _(des))  (13)

Therefore, for a spring stiffness of k₁=1.314 N/mm, l₃=72.62 mm andr_(des)=0 mm, the constant-force output is given as F=95.42N. Similarly,for, r_(des)=6.98 mm, F=104.6Nfor, r_(des)=13.08 mm, F=112.61Nfor, r_(des)=23.44 mm, F=126.22N

As is readily apparent by the three examples, the output force of theconstant force mechanism is adjustable by varying the length of thespring. This relationship may be graphically plotted, as shown in FIG.10.

Referring now to FIG. 5, an alternative constant force mechanismprovided in accordance with aspects of the present invention is shown,which is generally designated 38. The alternative mechanism 38 issimilar to the mechanism of FIGS. 1-3 in that it incorporates twosliders 12, 14, two springs 16, 18, and a link 20. However, a secondrigid link 40 is added to provide added space for mounting the sliders.The second rigid link 40 is connected, at one end, to the first slider12 via a rigid joint 42 and, at an opposite end, to the first rigid link20 via a revolute joint 44 The rigid joint 42 is a type that locks orfixes the short second rigid link 40 with the first slider 12 so thatthe link and the slider do not significantly rotate or move relative toone another, and preferably do not rotate or move relative to oneanother. The two sliders 12, 14 are shown in their respective homepositions in FIG. 5. In an alternative mechanism, the short second rigidlink 40 may be added to the second slider 14 and to the rigid link 20 toprovide added space. Still alternatively, two short rigid links 40 canbe added to both sliders 12, 14 to provide added space. The alternativemechanism 38 operates in the same manner and is covered by the sameprinciples discussed above with respect to the mechanism shown in FIGS.1-3.

The alternative mechanism 38 may also operate as an adjustable constantforce mechanism by varying the equilibrium position of the horizontalspring 16, such as by providing a preload to the spring by compressingor stretching the spring from its neutral position. Referring to FIG. 6,an adjustable constant-force mechanism 42 is shown comprising theconstant force mechanism 38 of FIG. 5 connected to an adjustable block45. In one exemplary embodiment, the adjustable block 45 comprises amovable head 46 movably connected to a base 48 via a rotatable device50. When the rotatable device 50 is rotated, it moves the movable head46 along the first axis 26 to change the equilibrium position of thespring 16. Hence, the horizontal spring 16, by moving the movable head46, is capable of moving a distance r_(des).

Although the adjustable block 45 is described with specificity as anadjustment means for adjusting the spring, a person of ordinary skill inthe art will recognize that numerous other modifications may be made orincorporated to permit adjustment of the equilibrium position of thespring 16. Accordingly, changes to the adjustable block 45 areconsidered within the spirit and scope of the present invention. Asexamples, telescoping devices with retention means such as a pin andhole arrangement may be used, simple gear train, and a cam and leversystem.

Verification of the output force of the adjustable constant forcemechanism of FIG. 6 was conducted using a stiffness of 1.314N/mm for thefirst and second springs 16, 18 and a fixed length of 72.62 mm for thelink 20. The extension link 40 has a free length of about 25 4 mm, whichwas arbitrarily selected and can vary depending on the desired mountingspacing for the slides 17, 19 and the sliders 12, 14. The stiffness ofthe two springs, which are the same, is found from the force-deflectioncurve obtained by testing the springs on a MTS Floor Testing Machine,which is a widely known device for force-deflection curve analysis.

Using the adjustable block 45 during the experiment, the length of thehorizontal spring 16 is changed to change its equilibrium position tothereby adjust the constant-force output. Although the results shownbelow are from decreasing the length of the spring (i.e., an increase inr_(des)), the length of r_(des) can be decreased (i.e., negative r_(des)value), which will lengthen the spring, placing it in tension in orderto decrease the desired output force. The results obtained from theexperiment on the adjustable constant-force mechanism 42 of FIG. 6 arepresented in FIG. 11.

The results are tabulated below:

Change % Desired Approximate in Change Force Experimental length r inOutput Force Output in mm. length in N. in N. r = 0 0 95.42 92 r = 6.989.61 104.6 100 r = 13.08 18.01 112.61 108 r = 23.44 32.27 126.22 118

The difference in the actual force output of the mechanism 42 of FIG. 6and the desired force output shown in FIG. 10 is due to the friction andinertia effects of the sliders 12. The high rise seen in the initialstage of FIG. 11 is perhaps due to the link 20 not immediatelytransmitting the input force from the horizontal slider 12 to thevertical slider 14, i.e. the load does not instantaneously jump fromzero to the desired output force. However, this lag can be furtheravoided by preloading the springs to the constant-force output value,i.e. starting from a point where the link transmits the desired forceaccurately. For example, slider 12 can have a mechanical limit whichdoes not allow it to fully reach the home position shown in FIG. 5. Ifthe mechanical limit or stop prevents the slider 12 from moving the fulllength of link 20, then the angle of the link 20 will be greater than180 degrees and both springs 16, 18 will be compressed storing energy.For example, in FIG. 11, the mechanical limit could be set to 72.62 mm-4mm (length of link 20 less 4 mm) to insure that the force is a constantoutput.

The above-described mechanisms may be made from a number of shapes,sizes, and materials. However, movements of the sliders 12, 14 should beconstrained to two perpendicular axes. Among the different options, twoperpendicular rails or tracks along with means for minimizing friction,such as linear ball bearing slides (e.g., drawer slides), may beincorporated for moving the sliders 12, 14. The different rail slidesmay be mounted on different surfaces and on different planes dependingon the particular mechanical connections used to constrain the sliders,to support the springs, to adjust the length of the horizontal spring 16(or vertical spring 18 if the horizontal spring 16 is not adjusted), tomake the desired slider configurations, etc. In addition, the adjustableblock 45 may incorporate a number of different configurations includinga simple motor system, a mechanical telescoping system, a hydrauliccylinder, etc. Accordingly, changes in the actual embodiment forproducing an adjustable constant force mechanism comprising two springsmounted on two perpendicular axes are within the spirit and scope of thepresent invention.

Exemplary applications for the adjustable constant force mechanismsdescribed elsewhere herein include adjustable constant force exerciseequipment, medical devices for therapy and rehabilitation, andelectrical connectors, just to name a few. For exercise equipment,pulleys, cables, chains, or belts, and various shaped bars may be usedas means for providing an input force to the input slider for bothpositive and negative weight training. In addition, by incorporating anadjustment block (e.g., block 45 in FIG. 6), the spring can be adjustedto vary the force resistance. The adjustable constant force mechanism ofthe present invention may similarly be incorporated in exerciseequipment to rehabilitate patients that have suffered from injuries ordiseases and have loss some range of motion, strength, balance, ordexterity. In another example, constant force mechanisms are used togravity balance and architectural lamp. Adjustable sliders can be usedto adjust the output force if the lamp becomes heavier due toalternations. In a third example, constant force mechanisms are used togravity balance arms such as robotic arms or even an exoskeleton tobalance a human arm. An adjustable compliant mechanism can be used tomake small alternations to the output force to balance the system.Typically, the exact weight and inertia is unknown so an adjustmentmethod is needed to balance the arm.

In U.S. Pat. No. 5,649,454 to Midha et al., referred to and expresslyincorporated herein by reference above, a host of constant forcemechanisms are described with flexural pivots and compliant links. Thesemechanisms produce a fixed constant force output. These mechanisms canbe adapted to produce adjustable outputs by adjusting the frame 12. Inparticular, in the compliant mechanisms of FIGS. 1 a, 1 d, 2 a-2 z, 3 a,3 b, and 4, one or more of the bases 12 may be moved or adjusted in thedirection of or against the direction of the input force (to compress orpush or to pull or put in tension) to preload at least one of theflexural joint, compliant connecting rod, or compliant crank to therebyproduce a different output force. FIG. 1 a of the '454 patent isreproduced in drawings section as FIG. 8 for reference.

Constant-force mechanisms may be adapted to operate in a miniaturized oreven a micro-level. Such a small scaled constant force mechanism has atleast two main advantages. Firstly, this mechanism will be able to applya constant-force even if there are small inevitable deflections, whichare difficult to determine and control at a micro-level. A constantforce mechanism is insensitive to micro-position errors. The secondadvantage at the micro-level is that the material structures arecompliant and will naturally behave like the springs in theabove-described analysis for the spring-based mechanisms. Using aminiature size constant force mechanism, a constant-force can be appliedfor different grasping and manipulation tasks.

Referring now to FIG. 7, a micro constant-force mechanism 52 provided inaccordance with aspects of the present invention is shown. The mechanism52 comprises a pair of slider crank mechanisms 53 working in tandem.Each crank mechanism comprises a pair of links 54, 56, a material link58, and three revolute joints 60, 62, 64. The two mechanisms 53 arejoined together by a center material link 66 and an output link 68. Thetwo links 54, 56 are positioned at an angle relative to one another,excluding 0 degree and 180 degrees.

In one exemplary embodiment, the pair of cranks 54, 56 and the outputlink 68 are rigid whereas the three material links 58, 58, 66 arecompressible or deformable. The four cranks 54, 56 are preferably ofequal lengths. In an exemplary embodiment, materials like plastics maybe used for the three material links 58, 58, 66, which will serve assprings in the constant-force mechanism 52 of FIG. 7. Elastomers havebeen developed and have been used successfully as highly compliantmaterial springs. Exemplary elastomers capable of performing ascompliant material springs include polycarbonate and arcylonitrile. Thematerial springs could either be linear springs or flexural members. Theflexural members are good for small force outputs as they are highlycompliant and thus can resist only smaller magnitude forces.

The constant force mechanism 52 of FIG. 7 may be made by assemblingcomponents made from conventional molding techniques. However, for MEMSapplication, such constant force mechanism may be made from siliconmicro-fabrication processes.

In the FIG. 7 mechanism 52, if a force is applied to the output link 68,the two horizontal links 58, 58 will flex. The compliant material in thecenter material link 66 will also act like a spring but will onlycompress in the vertical direction as the output link 68 is moved to theleft. The force relationship at the output may be described by thefollowing equation:F _(env)=2*K*l

Thus, much like the constant force mechanisms described with referenceto FIGS. 1-3 and 5, a mechanism made from an elastomeric material forsmall scale applications may also be incorporated to produce a constantforce output. These mechanisms can have an adjustable constant-forceoutput if the springs 58, 58 have an additional pre-load force caused byadjusting the equilibrium position.

Although the preferred embodiments of the invention have been describedwith some specificity, the description and drawings set forth herein arenot intended to be delimiting, and persons of ordinary skill the artwill understand that various modifications may be made to theembodiments discussed herein without departing from the scope of theinvention, and all such changes and modifications are intended to beencompassed within the appended claims. Various changes to theadjustable constant-force mechanisms may be made such as modifying thematerials, the size, the mechanical connections, the adjustmentmechanisms for adjusting the lengths of the springs, etc. to produce theforce relationship: F=k (1+r) and F=2*K*l. Other changes include using aresilient member instead of spiral wound metallic springs. For example,instead of an adjustment mechanism, a motor, cam, lever, pulley, or alocking mechanism comprising a pin and receptacle combination may beused to adjust the r_(des) length of the spring, which may in turnrequire the use of conventional mechanical devices such as gears,cables, belts, fasteners, and the like. Accordingly, many alterationsand modifications may be made by those having ordinary skill in the artwithout deviating from the spirit and scope of the invention.

1. A compliant mechanism comprising first and second support structureseach comprising a translational axis mounted perpendicular to oneanother; first and second resilient members, each comprising a lengthattached to first and second slidable structures, respectively,positioned on each support structure; a first link pivotally connecteddirectly or indirectly to each of the slidable structures, and anadjustment block attached to one of the structures for changing thelength of the resilient member of that structure, wherein the resilientmembers have an equal stiffness such that, in response to an appliedforce against the first slidable structure, the compliant mechanismprovides a substantially constant acting force against the applied forceas the slidable structures translate along a full length of eachrespective support structure.
 2. The compliant mechanism of claim 1,further comprising a second link connected to the first link and to oneof the slidable structures.
 3. The compliant mechanism of claim 1,wherein the adjustment block comprises a threaded rod.
 4. The compliantmechanism of claim 1, wherein the adjustment block comprises a movablehead mechanically linked to one of the resilient members for compressingor stretching the length of the resilient member.
 5. The compliantmechanism of claim 4, wherein one of the movable slider is connected toa mechanical connector for pushing on or pulling on by a user.
 6. Thecompliant mechanism of claim 1, wherein each support structure comprisesa linear ball bearing slide.
 7. A compliant mechanism for producing aconstant force during a range of motion of the mechanism comprising: afirst structure comprising a first movable slider adapted to move alonga first linear direction, a first resilient member comprising a lengthacting on the first slider so that the first slider experiences apushing force from the first resilient member during movement of thefirst slider along at least a portion of the first linear direction, asecond structure comprising a second movable slider adapted to movealong a second linear direction, a second resilient member comprising alength acting on the second slider so that the second slider experiencesa pushing force from the second resilient member during movement of thesecond slider along at least a portion of the second linear direction; alink comprising a length in pivotable relationship, either directly orindirectly, with both the first slider and the second slider; and anadjustment mechanism mechanically coupled to either the first resilientmember or the second resilient member for adjusting the length of thefirst resilient member or the second resilient member, wherein theresilient members have an equal stiffness such that, in response to anapplied force against the first slidable structure, the compliantmechanism provides a substantially constant acting force against theapplied force as the structures translate along a full length of eachrespective translational axis.
 8. The compliant mechanism of claim 7,wherein the first linear direction and second linear direction areperpendicular to one another.
 9. The compliant mechanism of claim 7,wherein the adjustment mechanism comprises at least one of a threadedrod or an adjustment pin.
 10. The compliant mechanism of claim 7,further comprising a second rigid link comprising a length.
 11. Thecompliant mechanism of claim 10, wherein the second rigid link isconnected to the first slider by a rigid joint, the link is connected tothe second rigid link by a revolute joint, and the link is connected tothe second slider by a revolute joint.
 12. The compliant mechanism ofclaim 10, further comprising a third rigid link comprising a length.